Low-Energy Spectrum of Electrons Scattered on Bound Electrons

The spectrum of electrons at low energies and large scattering angles resulting from the scattering of high-energy electrons on bound atomic electrons is calculated to lowest order in $\alpha Z$ and highest order in the incident energy. Relativistic Coulomb field effects are included by the use of wave functions correct to two orders in $\alpha Z$. Inclusion of these relativistic Coulomb effects leads to a cross section significantly different from that obtained previously by the use of the plane wave approximation. The results show that the low-energy spectrum of electrons scattered on bound atomic electrons completely dominates the peak predicted by Parzen and co-workers in the low-energy spectrum of bremsstrahlung-producing electrons.